Chiral sine-Gordon model

TL;DR

This paper analyzes the chiral sine-Gordon model using renormalization group techniques, revealing its phase structure, renormalizability, and connections to known models like the Kosterlitz-Thouless transition and matrix models.

Contribution

It demonstrates the renormalizability of the chiral sine-Gordon model and derives its beta functions, connecting it to established models and phase transition phenomena.

Findings

The model is renormalizable via perturbation expansion.

Beta functions have a bifurcation point dividing weak and strong coupling regions.

In the large-N limit, it reduces to the conventional sine-Gordon and $U(N)$ matrix models.

Abstract

We investigate the chiral sine-Gordon model using the renormalization group method. The chiral sine-Gordon model is a model for $G$-valued fields and describes a new class of phase transitions, where $G$ is a compact Lie group. We show that the model is renormalizable by means of a perturbation expansion and we derive beta functions of the renormalization group theory. The coefficients of beta functions are represented by the Casimir invariants. The model contains both asymptotically free and ultraviolet strong coupling regions. The beta functions have a zero which is a bifurcation point that divides the parameter space into two regions; they are the weak coupling region and the strong coupling region. A large-$N$ model is also considered. This model is reduced to the conventional sine-Gordon model that describes the Kosterlitz-Thouless transition near the fixed point. In the strong-coupling limit, the model is reduced to a $U(N)$ matrix model.